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Algebra / Linear Functions

Linear Functions

A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.

Least you need to know

  • The rate of change of a linear function is constant.
  • The slope between two points is change in output divided by change in input.

Key notation

  • $f(x)$ — The output of function $f$ for input $x$

Worked example

  • Use two function values to find the rate of change.
  • Substitute one point to find the initial value.

Common mistakes

  • Function notation asks for an output, not multiplication.
  • The initial value is the output when the input is 0.

How to recognize it

  • The problem mentions slope, rate of change, initial value, or function notation.

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Linear Functions

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